The only person in the CIS who knew Palpatine was Sidious was Dooku, I don't believe any other droid/general knew. Therefore, I don't know why Grievous DIDN'T inflict more damage on Coruscant. Sure, Dooku might have said "Don't do it," but after Dooku died, I'd get mad and order all Turbolasers to fire on the planet.

Heck, he could have even fired on the Jedi Temple if he didn't want to REALLY disobey the commander. Dooku wouldn't be able to object; he was a Sith, and it would have looked REALLY suspicious.

The planetary shield would prevent any such bombardment from succeeding.